With the growing interest in object categorization various methods have emerged that perform well in this challenging task, yet are inherently limited to only a moderate number of object classes. In pursuit of a more general categorization system our framework proposes a way to overcome the computational complexity encompassing the enormous number of different object categories by exploiting the statistical properties of the highly structured visual world. Our approach proposes a hierarchical acquisition of generic parts of object structure, varying from simple to more complex ones, which stem from the favorable statistics of natural images. The parts recovered in the individual layers of the hierarchy can be used in a top-down manner resulting in a robust statistical engine that could be efficiently used within many of the current categorization systems. The proposed approach has been applied to large image datasets yielding important statistical insights into the generic parts of object structure.

Another interesting issue is related to the construction of the above mentioned wavelets. The standard way of calculating their values uses an approximation based on Legendre polynomials and Bessel functions. We present a new method based on an eigenvalue problem for a matrix operator equivalent to that of the integral operator associated with the PS-wavelets. Its solution gives the values of these functions on the entire real line and is computationally more efficient.

The multi-scale and multi-orientation approach of the front-end visual system has become clear from psychophysical, neurophysiological and voltage-sensitive dye measurements. We will discuss the early visual stages as a mechanism / model, to do robust high order differential geometry on images, to perform perceptual grouping with oriented wavelets, and to extract subscenes from a scene with multi-scale singularity points.

The design of these algorithms is facilitated by the use of Mathematica as a high level analysis and visualization software.